A307443 G.f. A(x) satisfies: A(x) = Sum_{k>=0} k!*x^k*A(x)^k/(1 + x)^(k+1).

1, 0, 1, 3, 14, 73, 439, 2986, 22849, 195639, 1864072, 19639587, 227216485, 2866190328, 39155468153, 575750407431, 9063067630294, 152007287492665, 2705337486885751, 50909087031293746, 1009776468826520181, 21052688394533433215, 460223336063328374304, 10525518902412521320567

Offset: 0

Author

Ilya Gutkovskiy, Apr 08 2019

Keywords

• nonn

Examples

			G.f.: A(x) =  1 + x^2 + 3*x^3 + 14*x^4 + 73*x^5 + 439*x^6 + 2986*x^7 + 22849*x^8 + 195639*x^9 + 1864072*x^10 + ...
		

Crossrefs

Cf. A000166, A088368, A307441, A307442, A307444.

Programs

Mathematica

terms = 24; A[] = 1; Do[A[x] = Sum[k! x^k A[x]^k/(1 + x)^(k + 1), {k, 0, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]
terms = 24; A[] = 1; Do[A[x] = Sum[x^j Sum[(-1)^(j - k) k! Binomial[j, k] A[x]^k, {k, 0, j}], {j, 0, i}] + O[x]^i, {i, 1, terms}]; CoefficientList[A[x], x]

Formula

G.f. A(x) satisfies: A(x) = Sum_{j>=0} x^j * Sum_{k=0..j} (-1)^(j-k)*k!*binomial(j,k)*A(x)^k.

a(n) ~ exp(-1) * n!. - Vaclav Kotesovec, Apr 10 2019